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Elementary mathematics
Addition Multiplication Negative numbers From Wikipedia:Negative number Negative numbers are usually written with a minus sign in front. Negative numbers can be thought of as resulting from the subtraction of a larger number from a smaller. For example, negative three is the result of subtracting three from zero: :   −3.}} Addition Addition of two negative numbers is very similar to addition of two positive numbers. For example, :   −8}}. The idea is that two debts can be combined into a single debt of greater magnitude. When adding together a mixture of positive and negative numbers, one can think of the negative numbers as positive quantities being subtracted. For example: :   8 − 3     5}} and   7 − 2     5}}. Subtraction In general, subtraction of a positive number yields the same result as the addition of a negative number of equal magnitude. Thus :   5 + (−8)     −3}} and :   (−3) + (−5)     −8}} On the other hand, subtracting a negative number yields the same result as the addition a positive number of equal magnitude. (The idea is that losing a debt is the same thing as gaining a credit.) Thus :   3 + 5     8}} and :   (−5) + 8     3}}. Multiplication When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules: * The product of one positive number and one negative number is negative. * The product of two negative numbers is positive. Thus :   −6}} and :   6}}. Division The sign rules for division are the same as for multiplication. For example, :   −4}}, :   −4}}, and :   4}}. If dividend and divisor have the same sign, the result is always positive. Another method of dividing negative numbers is that if one of the numbers being divided is a negative, the answer will be negative. Elementary algebra : From Wikipedia:Elementary algebra: Elementary algebra builds on and extends arithmetic by introducing letters called variables to represent general (non-specified) numbers. Algebraic expressions may be evaluated and simplified, based on the basic properties of arithmetic operations ( , , , and ). For example, *Added terms are simplified using coefficients. For example, x + x + x can be simplified as 3x (where 3 is a numerical coefficient). *Multiplied terms are simplified using exponents. For example, x \times x \times x is represented as x^3 *Like terms are added together,Andrew Marx, Shortcut Algebra I: A Quick and Easy Way to Increase Your Algebra I Knowledge and Test Scores, Publisher Kaplan Publishing, 2007, , 9781419552885, 288 pages, page 51 for example, 2x^2 + 3ab - x^2 + ab is written as x^2 + 4ab , because the terms containing x^2 are added together, and, the terms containing ab are added together. *Brackets can be "multiplied out", using . For example, x (2x + 3) can be written as (x \times 2x) + (x \times 3) which can be written as 2x^2 + 3x *Expressions can be factored. For example, 6x^5 + 3x^2 , by dividing both terms by 3x^2 can be written as 3x^2 (2x^3 + 1) For any function f , if a=b then: * f(a) = f(b) * a + c = b + c * ac = bc * a^c = b^c One must be careful though when squaring both sides of an equation since this can result is solutions that dont satisfy the original equation. : 1 \neq -1 yet 1^2 = -1^2 A function is an if f(x) = f(-x) A function is an if f(x) = -f(-x) Back to top References